Theorem REF  allows us to study the deviations of \(T(X_1^n)\)  using the deviations of a sum of i.i.d centered random variables. We illustrate that we can then easily get sub-gaussian concentration as defined in  [1]} for Huber and Catoni's estimator. For simplicity's sake, we don't always search for the best possible bounds, better bounds are found and discussed in Section REF . We use concentration inequalities from [2]} and in particular Bernstein's inequality (Theorem 2.10 of [2]} reminded in Section  for completness).
